Bayesian Sample Size Determination Using Linex Loss and Linear Cost

Abstract

Sample size determination (SSD) is an important issue to consider when estimating any parameter. A number of researchers have studied the Bayesian SSD problem. One group considered utility (or loss) functions and cost functions in their SSD problem and the others did not. Among the former, most of the SSD problems are based on symmetric squared error (SE) loss function. On the other hand, in a situation when under estimation is more serious than overestimation or vice versa, then an asymmetric loss function should be used. In such a situation how many samples do we need to take to estimate the parameter under study? In this article, we consider sample size using the asymmetric linex loss function and a linear cost function for various distributions. We compare the sample size obtained from this asymmetric loss function with the sample size from the symmetric SE loss function. We also consider the situation where it is not worth sampling due to high sampling cost or strong prior information.